For me, it depends on the set, or what I'm doing to it.

For example, if my set is the set of all rational-valued sequences that tend to zero, I imagine a load of them "graphed" in front of me, overlapping. There are no specific examples in there, just a whole mass together.

Then if I want to check whether e.g. any of them can have terms that actually equal zero, I just take one, set a few terms to zero and see what happens. In this case, it still fits nicely within my set.

Or, for example, if my set is some arbitrary class X and I'm constructing its power set, I imagine a bunch of points in 2D space (maybe 15 but I'm not counting, it's just an arbitrary picture) and imagine someone has drawn a loop around e.g. 4 of them that will be in one subset. And then there are lots and lots of these loops, and those loops are the power set.

Don't try to imagine sets as the notation like {1, 3, 5}, as that doesn't get you anywhere unless you have a small, finite set like {1, 3, 5}. Of course, once you get your intuitive ideas by such imagery, you can formalize your ideas using proper set notation, logic etc. rather than these amorphous visual diagrams.